3 14.53 THEORETICAL SOIL MECHANICS VERTICAL STRESS INCREASE IN SOILS ANALYSIS METHODS - BOUSSINESQ (1883) Based on homogeneous, weightless, elastic, isotropic infinitely large halfspace free of initial stress and deformation. The modulus of elasticity is assumed constant and the principle of linear superposition is assumed valid (EM , 1990). Not accurate for layered soil stratigraphy with substantial thickness (NAVFAC DM7.01, 1986). Rigid Surface Layer Over Weaker Underlying Layer: If the surface layer is the more rigid, it acts as a distributing mat and the vertical stresses in the underlying soil layer are less than Boussinesq values. Weaker Surface Layer Over Stronger Underlying Layers: If the surface layer is less rigid than the underlying layer, then vertical stresses in both layers exceed the Boussinesq values. Revised 1/013 Slide 3 of 3

4 Revised 1/ THEORETICAL SOIL MECHANICS VERTICAL STRESS INCREASE IN SOILS ANALYSIS METHODS - WESTERGAARD Based on the assumption that the soil on which load is applied is reinforced by closely spaced horizontal layers which prevent horizontal displacement. The effect of the Westergaard assumption is to reduce the stresses substantially below those obtained by the Boussinesq equations. VERTICAL STRESS INCREASE IN SOILS ANALYSIS METHODS V:1H METHOD An approximate stress distribution assumes that the total applied load on the surface of the soil is distributed over an area of the same shape as the loaded area on the surface, but with dimensions that increase by an amount equal to the depth below the surface. Vertical stresses calculated V:1H method agree reasonably well with the Boussinesq method for depths between B and 4B below the foundation. Slide 4 of 3

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